At least 10 armed militants from the Al Qaeda-linked Somali terrorist group Al Shabaab had been keeping authorities at bay "in several locations" throughout the Westgate mall in the capital Nairobi, more than a day after they stormed the premises, killing scores of people.

The group was holding an unknown number of hostages, with Kenyan TV putting the figure at possibly 30.

"Most of the hostages have been released, and the Kenya Defence Forces (KDF) has taken control of most parts of the building," Kenyan military spokesman Colonel Cyrus Oguna told local television station KTN.

Kenyan troops continue to lay siege to the mall as they attempt to free the remaining hostages.

The ABC confirmed this morning that a Tasmanian man was among those killed by the gunmen.

He is understood to have been an architect who studied at the University of Tasmania.

The Department of Foreign Affairs says it is not yet appropriate to name the man and his family has asked for their privacy to be respected.

"The Australian Government has condemned this brutal terrorist attack in the strongest possible terms and expressed on behalf of the Australian people our deep regret for the senseless loss of life - not only to the Australian who's lost his life, but also to many other countries," he said.

More than 1,000 people were evacuated from the mall, with 200 of them taken to hospital.

Al Shabaab claims three attackers are from US

Al Shabaab militants said the the siege was retribution for Kenya's operations against the group in Somalia.

What is Al Shabaab?

Somali clan-based insurgent and terrorist group

Name translates to "The Youth" in Arabic

Leadership linked to Al Qaeda and members believed to have trained in Afghanistan

Members come from disparate clans, agenda not centralised

Imposes own version of Islamic law including dress regulations and public mutilations

Emerged out of insurgency fighting against Ethiopia, whose troops entered Somalia in 2006

Attacks focus on government officials and African Union Mission in Somalia

Claimed responsibility for many attacks in Mogadishu and central and northern Somalia

Carried out attack on UN base in Mogadishu in June

Source: United States National Counterterrorism Centre

The Kenyan government earlier said the group may include both male and female attackers and that one had died of his wounds after being arrested by security forces.

The ABC's North America correspondent Lisa Millar said it emerged this morning that the group was claiming three of the alleged attackers are from the United States.

"You can imagine that is raising a whole lot of questions here amongst the intelligence community about this group and what went on in the lead-up to this attack," she said.

US secretary of state John Kerry said the siege highlighted the gravity of the threat posed by Somali militants.

He said he had spoken with Somalia's foreign minister and ambassador to Washington earlier in the day about the attack.

"It represents the seriousness and the breadth of the challenge we face with ruthless and completely reckless terrorists," Mr Kerry told reporters as he started a meeting in New York with Egypt's foreign minister Nabil Fahmy.

"It's an enormous offense against everybody's sense of right and wrong."

Mr Kerry said several US citizens had been hurt and the wife of a US diplomat working for a US development agency was killed.

He said he had also spoken with Somalia's foreign minister Fawzia Adan and its ambassador to Washington, Elmi Duale, about the crisis.

US president Barack Obama called Kenyan president Uhuru Kenyatta to express his condolences for the "terrorist attack" and offered support to bring the perpetrators to justice.

Mr Kenyatta - who himself lost a nephew and the nephew's fiancé in the attack - vowed to hold firm in what he called the "war on terror" in Somalia and said, cautiously, that Kenyan forces could end the siege.

"I assure Kenyans that we have as good a chance to successfully neutralise the terrorists as we can hope for," he said.

"We will punish the masterminds swiftly and painfully."

But a military spokesman for Al Shabaab said his group had nothing to fear.

"Where will Uhuru Kenyatta get the power with which he threatened us?" Sheikh Abdiasis Abu Musab said.